Rest and Motion
Definition
Rest and motion are relative terms which actually depend on the observer.
A body is said to be at rest if its position does not change with time with respect to the observer.
Similarly, A body is said to be in motion if its position changes with time with respect to the observer.
The same body may be at rest with respect to one observer while in motion with respect to some other observer. For example. A briefcase in a moving train is at rest with respect to a person sitting in train but in motion with respect to any person standing outside.
Note : Unless stated in a problem we consider by default an observer to be stationary with respect to ground, trees, a stationary table, pole etc.
For example : If it is said that a car is moving, then we suppose observer to be at rest with respect to ground.
Scalar and vector
Introduction :
In Physics, we deal with the quantities which can be measured. We call them “Physical quantites”. Hence every physical quantity can be measured.
Measurement of a quantity is expressed in terms of a number and unit. The unit represents the nature of the quantity and the number represents the magnitude (amount). Physical quantities are of two types as explained below.
Scalar :
A physical quantity, having only magnitude, is called a scalar quantity or simply a scalar (It is completely specified by the magnitude) like distance, time , mass , energy , current , pressure , charge etc. It is denoted by just a symbol,
For example : Speed = ‘v’, Distance = ‘s’, Time = ‘t’
Vector :
A physical quantity, having magnitude as well as direction, is called a vector quantity or simply a vector like displacement, velocity, force, etc. It is denoted by an arrow on symbol.
For example : Displacement = ‘\mathop s\limits^ \to ’, Velocity = ‘\mathop v\limits^ \to ’, Acceleration = ‘\mathop a\limits^ \to ’
Difference between Scalar and Vector :
| Scalar Quantities | Vector Quantities |
|---|---|
| These are completely specified by their magnitude only. | These are completely specified by their magnitude as well as direction. |
| These change by change in their magnitude only. | These change by change of their either magnitude or direction or both. |
| These are added or subtracted by laws of ordinary algebra. | These are added or subtracted by laws of vector algebra. |
Difference between distance and displacement
In everyday language, the words distance and displacement are used in the same sense but in physics these two words have different meanings. Let us understand this difference by taking an example.
Figure
Distance travelled = 5 + 3 = 8 km
Displacement = 4 km towards East.
Suppose a man lives at place A and he has to reach another place C, (see figure) but first he has to meet his friend living at place B. Now, the man starts from point A and travels a distance of 5 km to reach B and then travels another 3 km from B to reach C. Thus, the man goes along the path ABC (shown by dotted lines). Length of the path ABC gives us the actual distance travelled by the man. Thus, the distance travelled by a body is the actual length of the path covered by a moving body irrespective of the direction in which the body travels. For example, in this case, the actual length of the path covered by the man is 5 km + 3 km = 8 km, so the distance travelled by the man is 8 km.
We will now discuss this problem in a different way. When the man has reached point C, we want to know how far he is now from the starting point A, that is, we want to know the shortest distance between point A and point C. Let us draw a straight line AC between A and C. The length of the straight line path AC (which is 4 km here) is the displacement of the man from point A, that is, on reaching C, the man is only 4 km away from the starting point A. This displacement is in the East direction. Thus, when a body moves from one point to another, the distance travelled refers to the actual length of the indirect path whereas displacement refers to the actual length of the shortest path from one point to another point. So, whatever be the actual length of the path followed by a moving body, displacement of the body is always represented by the shortest distance between the initial and final positions of the body.
Thus, when a body moves from one position to another, the shortest (straight line) distance between the initial position and final position of the body, alongwith direction, is known as its displacement. In the above example, the shortest distance between the initial position A and final position C of the man is 4 km, so the displacement of man is 4 km in the East direction. It is clear that the distance travelled has only magnitude whereas displacement has magnitude as well as direction. Odometer is a
device used to read distance. Let us consider one more example :
Suppose a person moves in a circular path centered at O. He starts from A and reaches diametrically opposite point B. Then
(a) Distance = Length of actual circular path from A to B = Half the circumference
i.e. Distance = \frac{{2\pi r}}{2} = \pir
as r = 1m
∴ Distance = \pim
(b) Displacement = 2r along west.
= 2m along west
DISTANCE, DISPLACEMENT DIFFERENCE TABLE
| Distance | Displacement |
|---|---|
| Distance is the length of the path actually traveled by a body in any direction | Displacement is the shortest distance between the initial and the final positions of a body in the direction of the final position |
| Distance is always positive | Displacement may be positive as well as negative and even zero |
| Distance is a scalar quantity | Displacement is a vector quantity |
Direction sense in case of straight line motion
In case of straight line motion, an object may have only two directions of motion. One may be taken as positive direction and other as negative direction.
Generally rightwards and upwards are taken as positive direction while leftwards and downwards are taken as negative directions as shown :
Figure
Thus if a body is displaced towards right of its starting point, its displacement is positive and if a body is displaced towards left of its starting point, its displacement is negative.
Similar is the case for upward and downward displacement.
Let us understand this more clearly by following examples :
(a) Suppose a person drops a ball from a cliff 100 m high. Then final displacement of ball is –100 m.
Figure
If a man goes 10 m along east i.e. O to A and then turns back and moves along the same path but now moves 25 m in west direction i.e. A to B, then his displacement is OB i.e. either 15 m along west or –15 m
Figure